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Two point like objects each with mass m ...

Two point like objects each with mass m are connected by a massless rope of length `l` the object are suspended vertically near the surface of earth, so that one object hanging below the other then the objects are relased. Show that the tension in the rope is `T=(GMml)/(R^(3))` where M is the mass of the earth and R is its radius `|l lt lt R|`

Text Solution

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The correct Answer is:
n/a

`mg-T=ma` ..(1)
`T+mg'=ma` …(2)
by adding (1) and (2)
`a=(g+g')/(2),T=(m(g+g))/(2)-mg'`
`T=m((g-g')/(2))=(m)/(2)[g-g[1-(2h)/(R)]]`
`T=(mg)/(2)(2l)/(R)=(mgl)/(R)=(GMml)/(R^(3))`
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